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http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/10119完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 許順吉(Shuenn-Jyi Sheu) | |
| dc.contributor.author | Shiu-Tang Li | en |
| dc.contributor.author | 李旭唐 | zh_TW |
| dc.date.accessioned | 2021-05-20T21:03:22Z | - |
| dc.date.available | 2011-08-09 | |
| dc.date.available | 2021-05-20T21:03:22Z | - |
| dc.date.copyright | 2011-08-09 | |
| dc.date.issued | 2011 | |
| dc.date.submitted | 2011-07-14 | |
| dc.identifier.citation | [1] P. Ney, F. Spitzer: The Martin Boundary for Random Walk. Transactions of the American Mathematical Society Vol. 121, No. 1 (Jan., 1966), pp. 116-132.
[2] F. Spitzer: Principles of random walk. 2nd Edition. Graduate texts in mathematics, Springer-Verlag, New York, 1976. [3] S. A. Sawyer: Martin boundaries and random walks. In Adam Koranyi (Ed.), Harmonic functions on trees and buildings. Contemporary Mathematics 206, American Mathematical Society, Providence, pp17-44, 1997. [4] W. Woess: Random walks on in nite graphs and groups. Cambridge University Press, New York, 2000. [5] R. R. Phelps: Lectures on Choquet's theorem. 2nd Edition. Springer-Verlag, New York, 2001. [6] J. Munkres: Topology. 2nd Edition. Prentice Hall, Inc., Upper Saddle River, NJ, 2000. [7] John G. Kemeny, J. Laurie Snell, Anthony W. Knapp: Denumerable Markov chains. 2nd Edition. Graduate texts in mathematics, Springer-Verlag, New York, 1976. [8] E.B. Dynkin: Markov processes and related problems of analysis. Cambridge University Press, New York, 1982. [9] K. L. Chung: A Course in probability theory. 3rd Edition. Academic Press, San Diego, 2001. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/10119 | - |
| dc.description.abstract | 在這篇論文中我們探討一個具有兩個變量 $lambda,w$ 的方程組 $sum_{y in
S}p(x,y)exp ig(h(y)-lambda+w(y) ig) = exp(w(x))$, 其中 $p$ 是一個狀態空間為 $mathbb Z^d$ 的馬可夫鏈的轉移機率, 且不論從任何狀態出發, $p$ 只會轉移至有限多個狀態. 當 $h equiv 0$, $lambda =0$ 之情況下所解出的 $exp(w(x))$ 即是此轉移機率 $p$ 的調和函數. 本論文的目標旨在探討 $lambda$ 之範圍, 以及當 $lambda$ 給定時其對應之 $w$ 為何. 當 $h equiv 0$ , 且 $p$ 為一隨機漫步之轉移機率時, 我們將更進一步給出 $(lambda,w)$ 之明確表現形式. | zh_TW |
| dc.description.provenance | Made available in DSpace on 2021-05-20T21:03:22Z (GMT). No. of bitstreams: 1 ntu-100-R98221016-1.pdf: 967113 bytes, checksum: 1a51d3c6c5797fad66a5bb1f7f6d31bf (MD5) Previous issue date: 2011 | en |
| dc.description.tableofcontents | 目 錄
Contents 口試委員會審定書 誌謝……………………………………………………………………………… ii 中文摘要……………………………………………………………………… iv 英文摘要………………………………………………………………………… v 1. Introduction…………………………………………………………………… 1 2. The structure of all solutions (lambda,w) …………………………… 4 2.1 Proof of theorem 2.1.…………………………………………………… 5 2.2 The greatest lower bound of all possible lambda 's is finite………………… 9 2.3 The greatest lower bound of all possible lambda 's is a solution ……… 10 2.4 Restrictions on h such that (1) has solutions ………… 12 2.5 Some properties of w(x) when certain restrictions on h(x) are imposed ………………………………………………………… 13 3. The pˆlambda,w transformations …………………………………… 15 3.1 The transience, recurrence, and positive recurrence of pˆlambda,w … 15 3.2 Criteria for when all harmonic functions are constants ……………… 23 4. Estimates for some lower bound for all l 's such that (l,w) is a solution of (1) under some conditions …………………………………………… 26 4.1 Local central limit theorem …………………………………… 26 4.2 Lower bound for all lambda 's such that (lambda,w) is a solution of (1) ……………… 34 5. One step further about the solution structure ……………………………… 38 5.1 The solution structure: general case ……………………… 38 5.2 The solution structure when h(x) o 0………………………………… 41 6. Miscellaneous examples ………………………………………………… 46 6.1 An example: h(y) − lambda 0 < −d for all |y|> M………………………… 46 6.2 An example: h(y) − lambda 0 > d for all |y|> M………………………… 46 6.3 An example: Both 0 {y : h( y) − l > d} and #{y : h( y) − l < −d} are infinite……………………………………………………………… 47 參考文獻 (References)…………………………………………………… 48 附錄 (Appendix) ……………………………………………………… 49 A.1 Introduction …………………………………………………… 49 A.2 Construction of Martin boundary ………………………………… 50 A.3 Harmonic measure ……………………………………………… 52 A.4 h-process transform ………………………………………… 60 A.5 Regular boundary and minimal boundary………………………… 61 | |
| dc.language.iso | en | |
| dc.title | 一個馬可夫鏈的特徵值問題及其應用 | zh_TW |
| dc.title | An Eigenvalue Problem for Markov Chains
With Applications | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 99-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.coadvisor | 張志中(Chih-Chung Chang) | |
| dc.contributor.oralexamcommittee | 姜祖恕(Tzuu-Shuh Chiang),陳冠宇(Guan-Yu Chen) | |
| dc.subject.keyword | 馬可夫鏈,隨機漫步,平賭序列,暫態,再生態,調和函數,局部中央極限定理,Choquet定理,Martin 邊界, | zh_TW |
| dc.subject.keyword | Markov chain,random walk,martingale,transient,recurrent,harmonic functions,local central limit theorem,Martin boundary, | en |
| dc.relation.page | 68 | |
| dc.rights.note | 同意授權(全球公開) | |
| dc.date.accepted | 2011-07-14 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 數學研究所 | zh_TW |
| 顯示於系所單位： | 數學系 | |
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